Communication device for performing differential phase shift keying based on a plurality of previous signals and operating method thereof

ABSTRACT

An method of determining a symbol according to a phase difference between input signals input in order of time may include calculating a first phase difference between a phase of a first previous signal received prior to a target signal and a phase of a second previous signal received prior to the first previous signal; calculating a second phase difference between a phase of the target signal and the phase of the second previous signal; calculating target likelihoods based on the first phase difference and the second phase difference; and determining an expected phase difference between the target signal and the first previous signal or an expected symbol for the target signal, based on the target likelihoods.

CROSS-REFERENCE TO RELATED APPLICATION

This application is based on and claims priority under 35 U.S.C. §119 toKorean Patent Application No. 10-2021-0108180, filed on Aug. 17, 2021,in the Korean Intellectual Property Office, the disclosure of which isincorporated by reference herein in its entirety.

BACKGROUND

One or more embodiments of the present disclosure relate tocommunication devices for wireless communication, and more particularly,to communication devices configured to perform differential phase shiftkeying (DPSK).

DPSK refers to a digital modulation technology (e.g., modulation anddemodulation technology) for determining currently received symbol databased on a phase difference corresponding to two consecutive symbols.DPSK technology may convey data by changing (e.g., modulating) the phaseshift of each symbol with respect to the phase of the previous symbolsent. For example, in a communication device configured to performBluetooth communication, a phase difference of an enhanced data rate(EDR) packet may be a DPSK symbol. In some aspects, when a communicationdevice receives a signal including a phase error, the phase erroraffects both previous and subsequent symbols. Moreover, once a symbolerror occurs, error propagation may result (e.g., where many or all ofthe subsequent symbols may be affected by the symbol error).

Some devices may implement error-detecting code, such as a cyclicredundancy check (CRC), to detect accidental or unintentional changes toraw data. When a communication device performs CRC correction, asoft-output of a demodulator may reflect a relative reliabilitydifference between information bits in a packet to operate normally.When error propagation occurs, accuracy of such reliability regardingthe soft-out may decrease. Accordingly, there is a need in the art forimproved wireless communication (e.g., DPSK) techniques.

SUMMARY

One or more embodiments of the present disclosure may provide a methodof determining a symbol accurately corresponding to a phase differencewith high reliability to reduce error propagation occurring indifferential phase shift keying (DPSK).

According to an aspect of the present disclosure, there is provided amethod of determining a symbol according to a phase difference betweeninput signals input in order of time, the method including: calculatinga first phase difference between a phase of a first previous signal anda phase of a second previous signal, wherein the first previous signalis received prior to a target signal, and wherein the second previoussignal is received prior to the first previous signal; calculating asecond phase difference between a phase of the target signal and thephase of the second previous signal; calculating, based on the firstphase difference and the second phase difference, target likelihoodsthat a phase difference between the target signal and the first previoussignal corresponds to each of a plurality of symbols; and determining,based on the calculated target likelihoods, an expected symbol for thetarget signal or an expected phase difference between the target signaland the first previous signal.

According to another aspect of the present disclosure, there is provideda method of determining a symbol corresponding to an input signal, themethod including: generating a first phase difference between a firstinput signal and a previous signal, wherein the first input signal isinput in a previous sequence preceding a target sequence, and whereinthe previous signal is received prior to the previous sequence;generating a second phase difference between a second input signal andthe previous signal, wherein the second input signal is input in thetarget sequence; and determining an expected phase difference betweenthe second input signal and the first input signal based on the firstphase difference and the second phase difference.

According to another aspect of the present disclosure, there is provideda communication device including: a first phase difference calculatorconfigured to calculate a first phase difference between a phase of afirst previous signal and a phase of a second previous signal, whereinthe first previous signal is received prior to a target signal, andwherein the second previous signal is received prior to the firstprevious signal; a second phase difference calculator configured tocalculate a second phase difference between a phase of the target signaland the phase of the second previous signal; a target likelihoodgenerator configured to generate target likelihoods that a phasedifference between the target signal and the previous first previoussignal corresponds to each of a plurality of symbols based on the firstphase difference and the second phase difference; and an expected valuedeterminer configured to determine, based on the target likelihoods, andexpected symbol for the target signal or an expected phase differencebetween the target signal and the first previous signal.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present disclosure will be more clearly understoodfrom the following detailed description taken in conjunction with theaccompanying drawings in which:

FIG. 1 is a block diagram of a communication system according to anembodiment;

FIG. 2 is a block diagram of a configuration of a receiver configured toreceive and demodulate an input signal according to an embodiment;

FIG. 3 is a diagram illustrating resource elements including symbolsaccording to an embodiment;

FIG. 4 is a flowchart illustrating a method of calculating a first phasedifference and a second phase difference, based on a plurality ofprevious signals, according to an embodiment;

FIG. 5 is a diagram of a phase difference calculating module accordingto an embodiment;

FIG. 6 is a flowchart illustrating a method of calculating ahard-decision phase difference according to an embodiment;

FIG. 7 is a graph showing a hard-decision phase difference of a phasedifference calculated according to an embodiment;

FIG. 8 is a diagram illustrating signals which a phase differencecalculating module receives in each sequence according to an embodiment;

FIG. 9 is a flowchart illustrating a method of determining an expectedphase difference or an expected symbol by calculating a targetlikelihood according to an embodiment;

FIGS. 10 and 11 are block diagrams illustrating a configuration of aphase-to-symbol likelihood generating module according to embodiments;

FIG. 12 is a block diagram illustrating a configuration of an expectedsymbol determiner according to an embodiment;

FIG. 13 is a flowchart illustrating a method of calculating firstlikelihoods and second likelihoods according to an embodiment;

FIG. 14 is a flowchart illustrating a method of selecting at least someof first likelihoods and second likelihoods from a lookup tableaccording to an embodiment; and

FIG. 15 is a block diagram illustrating components of a communicationdevice according to an embodiment.

DETAILED DESCRIPTION OF THE EMBODIMENTS

DPSK refers to a digital modulation technology (e.g., modulation anddemodulation technology) for determining currently received symbol databased on a phase difference corresponding to two consecutive symbols.DPSK technology may convey data by changing (e.g., modulating) the phaseshift of each symbol with respect to the phase of the previous symbolsent. However, when a communication device receives a signal including aphase error, the phase error may affect both previous symbols andsubsequent symbols. Moreover, once a symbol error occurs, errorpropagation may result where multiple symbols (e.g., many or all of thesubsequent symbols) may be affected by the symbol error.

In some examples, to prevent such error propagation, a communicationdevice may conduct (e.g., determine) hard-decision techniques on phasedifferences of consecutive signals. After the hard-decision, the phasedifferences may be accumulated to calculate a difference with a phase ofa target signal. Even in such examples, there still is a possibility ofincorrect correspondence to a symbol by the communication device (e.g.,and errors may thus not be corrected even through implementation oferror-detecting code, such as a cyclic redundancy check (CRC)correction).

According to the techniques described herein, a communication device maymore efficiently determine a symbol of a target signal obtained in atarget sequence (e.g., a current sequence). For instance, acommunication device may determine a symbol of a target signal (obtainedin a target sequence) based on phases of previous signals (obtained in aplurality of previous sequences) to accurately determine a symbol of atarget signal corresponding to a calculated phase difference. Forexample, the communication device may calculate a phase difference of aplurality of previous signals, as well as a phase difference between thetarget signal and a previous signal. The communication device mayfurther calculate a likelihood that the two phase differences correspondto each symbol (e.g., and the communication device may calculate anexpected value for the target signal based on the likelihood that thephase difference corresponds to each symbol).

As an example, a communication device may use input signals received ina plurality of previous sequences preceding a target sequence in orderto determine a symbol corresponding to an input signal received in thetarget sequence. For instance, a communication device may determine afirst phase difference PD1 and a second phase difference PD2, where thefirst phase difference PD1 is calculated between a first previous signaln - 1 and a second previous signal n - 2, and the second phasedifference PD2 is calculated between a target signal n and the secondprevious signal n - 2. As described in more detail herein, thecommunication device may then determine an expected phase difference EPDand/or an expected symbol ES for the target signal, based on thecalculated first phase difference PD1 and the second phase differencePD2.

Hereinafter, embodiments of the present disclosure will be described indetail with reference to the accompanying drawings.

FIG. 1 is a block diagram of a communication system according to one ormore embodiments of the present disclosure.

With reference to FIG. 1 , a communication system may include a firstcommunication device 1 and a second communication device 2 configured towirelessly communicate through a channel (e.g., a wirelesscommunications channel). Generally, the system of FIG. 1 may be anysystem for wireless communication. In some embodiments, the system maybe a wireless communication system such as a 5th generation (5G)wireless system, a long term evolution (LTE) system, a WiFi system,etc., but the system is not limited thereto. In some embodiments, thesystem may be a wired communication system such as a storage system, anetwork system, etc. Hereinafter, aspects of the system may refer toaspects of a wireless communication system, but embodiments of thepresent disclosure are not limited thereto.

For example, the first communication device 1 may be a base station or acomponent included in a base station. The base station may refer to afixed station which communicates with a terminal and/or other basestations, and may transmit and receive data and/or control informationby communicating with a terminal and/or other base stations. The basestation may be referred to as a Node B, an evolved-Node B (eNB), a basetransceiver system (BTS), an access point (AP), a relay node, a remoteradio head (RRH), a radio unit (RU), a small cell, etc.

For example, the second communication device 2 may be a terminal or acomponent included in a terminal. The terminal may be a wirelesscommunication device, and may refer to various devices capable oftransmitting and receiving data and/or control information bycommunicating with the first communication device 1. For example, theterminal may be referred to as a user equipment, a mobile station (MS),a mobile terminal (MT), a user terminal (UT), a subscriber station (SS),a wireless device, a handheld device, or some other suitable processingdevice.

As another example, the first communication device 1 may be a terminalor a component included in a terminal, and the second communicationdevice 2 may be a base station or a component included in a basestation. As another example, the first communication device 1 and thesecond communication device 2 may be a terminal or a component includedin a terminal (e.g., the first communication device 1 and the secondcommunication device 2 may each be terminals or components included interminals).

The wireless communication network (e.g., between the firstcommunication device 1 and the second communication device 2) maysupport communication among a plurality of users by sharing availablenetwork resources. For example, in a wireless communication network,information may be transmitted through various methods, such as codedivision multiple access (CDMA), frequency division multiple access(FDMA), time division multiple access (TDMA), orthogonal frequencydivision multiple access (OFDMA), single carrier frequency divisionmultiple access (SC-FDMA), etc.

The first communication device 1 and the second communication device 2may communicate with each other via uplink UL (e.g., from a terminal toa base station) and downlink DL (e.g., from a base station to aterminal) communications. In a wireless system such as an LTE system andan LTE-Advanced system, the uplink and the downlink may transmit andreceive control information through a control channel such as a physicaldownlink control channel (PDCCH), a physical control format indicatorchannel (PCFICH), a physical hybrid ARQ indicator channel (PHICH), aphysical uplink control channel (PUCCH), an enhanced physical downlinkcontrol channel (EPDCCH), etc., and may transmit and receive datathrough a data channel such as a physical downlink shared channel(PDSCH), a physical uplink shared channel (PUSCH), etc. Also, thecontrol information may be transmitted by using the EPDCCH (enhancedPDCCH or extended PDCCH).

In addition, each of the first communication device 1 and the secondcommunication device 2 may be a device including user equipment, and maytransmit and receive information through a communication method such asnear field communication (NFC), Bluetooth, etc. Each of the firstcommunication device 1 and the second communication device 2 may includean NFC controller for use of NFC and a Bluetooth controller for use ofBluetooth. The first communication device 1 may generate a radiofrequency (RF) signal corresponding to generated information andtransmit the RF signal to the outside through at least one antenna. Thesecond communication device 2 may receive the RF signal through at leastone antenna, and provide information corresponding to the RF signal to aprocessor included in the second communication device 2.

The first communication device 1 may include a modulator 11, atransceiver 12, and an antenna. The modulator 11 may convert digitalinformation into an RF signal, which is an analog signal. For example,when the modulator 11 modulates digital information into an analogsignal based on DPSK, an analog signal having a phase differencecorresponding to the digital information may be generated. Thetransceiver 12 may perform time-to-frequency conversion on a receivedsignal or perform frequency-to-time conversion on a transmission signal.Further, the transceiver 12 may include an analog down-conversion mixer,and generate a baseband signal by down-converting a frequency of areceived signal (or a data signal). The first communication device 1 maytransmit an RF signal through a transmission antenna.

The second communication device 2 may include a demodulator 21, atransceiver 22, and an antenna. The second communication device 2 mayreceive an RF signal through a receiving antenna. The transceiver 22 ofthe second communication device 2 may obtain a signal of a frequency tobe read by performing the time-to-frequency conversion on the receivedRF signal. The demodulator 21 may generate digital information based onthe RF signal obtained by the transceiver 22. For example, when thedemodulator 21 demodulates digital information from an analog signalbased on DPSK, digital information may be generated based on a phasedifference of received consecutive analog signals.

A transceiver (e.g., transceiver 12 and transceiver 22) may communicatebi-directionally, via antennas, wired, or wireless links as describedabove. For example, a transceiver (e.g., transceiver 12 and transceiver22) may represent a wireless transceiver and may communicatebi-directionally with another wireless transceiver. A transceiver mayalso include or be connected to a modem to modulate the packets andprovide the modulated packets to for transmission, and to demodulatereceived packets (e.g., as described in more detail herein in accordancewith one or more aspects of the described techniques). In some examples,transceiver 12 and/or transceiver 22 may be tuned to operate atspecified frequencies. For example, a modem of a communication devicemay configure a transceiver to operate at a specified frequency andpower level based on the communication protocol used by the modem.

The demodulator 21 according to one or more embodiments of the presentdisclosure may use input signals received in a plurality of previoussequences preceding a target sequence to determine a symbolcorresponding to an input signal received in the target sequence. Thedemodulator 21 may calculate a first phase difference between an inputsignal received in a first previous sequence and an input signalreceived in a second previous sequence preceding the first previoussequence, and the demodulator 21 may calculate a second phase differencebetween an input signal received in a target sequence and an inputsignal received in the second previous sequence. The demodulator 21 maydetermine an expected phase difference between a signal input in thetarget sequence and a signal input in the first previous sequence bycalculating a likelihood that each of the first phase difference and thesecond phase difference corresponds to each of a plurality of symbols.According to one embodiment, the expected phase difference may bereferred to as a soft-decision value.

In DPSK, a modulated signal’s phase may be shifted relative to aprevious signal element (e.g., rather than relative to a referencesignal, a signal phase may follow a low state or a high state of aprevious signal element). For DPSK modulation, a transmitted signalitself (e.g., preceding signal elements) may be used as the “referencepoint” for signal modulation.

Generally, for DPSK demodulation, the phase between two successivereceived symbols is compared and used to determine what the data musthave been (e.g., demodulator 21 may compare the phase of a reversed bitwith the phase of a previous bit). For instance, upon reception, thereceived symbols are not decoded one-by-one to constellation points.Instead, demodulator 21 may compare received symbols (e.g., the phasesof received symbols) directly to one another to interpret (e.g.,demodulate) received data.

FIG. 2 is a block diagram of an example configuration of a receiverconfigured to receive and demodulate an input signal IN according to anembodiment.

With reference to FIG. 2 , the demodulator 21 may include a phasedifference calculating module 210 and a phase-to-symbol likelihoodgenerating module 220. According to an embodiment, the phase differencecalculating module 210 may receive an input signal IN in each sequenceand calculate a phase difference between the received input signal INand input signals IN received in a plurality of previous sequences. Thesequence may be a time interval allocated in correspondence with eachsymbol, and a length of each sequence may be predefined in acommunication system.

According to an embodiment, the phase difference calculating module 210may output as a first phase difference PD1 a phase difference between atarget signal input in a target sequence and a first previous signalreceived in a first previous sequence preceding the target sequence byone sequence. The phase difference calculating module 210 may output asa second phase difference PD2 a phase difference between a secondprevious signal received in a second previous sequence preceding thefirst previous sequence by one sequence and the target signal (e.g., thesecond previous sequence preceding the target sequence by twosequences). That is, the first phase difference PD1 may be a phasedifference between input signals IN received consecutively, and thesecond phase difference PD2 may be a phase difference between inputsignals IN received in sequences apart from each other by two sequences.Hereinafter, a target sequence is described as preceding a firstprevious sequence by one sequence, and the first previous sequence isdescribed as preceding a second previous sequence by one sequence;generally however, sequence differences of the present disclosure arenot limited thereto.

According to an embodiment, a phase of the first previous signal and aphase of the second previous signal may be an input signal IN receivedin each sequence; however, according to another embodiment, the phase ofthe first previous signal and the phase of the second previous signalmay be a sum of phase differences generated in each previous sequencesince the reception of the input signal IN, and the phase differencesgenerated in each sequence may be hard-decision phase differences. Thehard-decision phase difference is described in more detail herein (e.g.,at least with reference to FIGS. 6 and 7 ).

The phase-to-symbol likelihood generating module 220 may receive thefirst phase difference PD1 and the second phase difference PD2 generatedfrom the phase difference calculating module 210, and phase-to-symbollikelihood generating module 220 may determine an expected phasedifference EPD and/or an expected symbol ES for a target signal, basedon the received first phase difference PD1 and the second phasedifference PD2. At this time, the phase-to-symbol likelihood generatingmodule 220 may delay the first phase difference PD1 by one sequence.That is, in some examples, the phase-to-symbol likelihood generatingmodule 220 may determine the expected phase difference EPD or theexpected symbol ES, based on the first phase difference PD1 between thefirst previous signal and the second previous signal and the secondphase difference PD2 between the target signal and the second previoussignal in a target sequence.

According to an embodiment, the phase-to-symbol likelihood generatingmodule 220 may calculate first likelihoods that the first phasedifference PD1 corresponds to each of a plurality symbols, and calculatesecond likelihoods that the second phase difference PD2 corresponds toeach of the plurality of symbols.

In some examples, Bluetooth EDR packet payloads may include data symbolsrepresented by phase variations (e.g., in a transmitted or receivedradio frequency (RF) signal). DQPSK can be used to modulate the payloadof a Bluetooth EDR packet (e.g., where a phase of a current symbol, or atarget symbol, may be indicated with reference to a phase of a precedingsymbol, or a phase of one or more previous signals).

For example, a communication device configured to perform Bluetoothcommunication may calculate a likelihood that each phase differencecorresponds to two symbols in enhanced data rate (EDR) EDR2 mode and alikelihood that each phase difference corresponds to each of foursymbols in EDR3 mode. The phase-to-symbol likelihood generating module220 may calculate a target likelihood, based on first likelihoods andsecond likelihoods, and determine the expected symbol ES based on thetarget likelihood and information per bit of each symbol or the expectedphase difference EPD, based on the target likelihood and a phasecorresponding to each symbol.

In some aspects, the phase difference calculating module 210 and thephase-to-symbol likelihood generating module 220 may include differenthardware modules. However, the described techniques are not limitedthereto, and the phase difference calculating module 210 and thephase-to-symbol likelihood generating module 220 may include differentsoftware modules provided in one hardware module (e.g., the phasedifference calculating module 210 and the phase-to-symbol likelihoodgenerating module 220 may include software that, when compiled andexecuted, cause a single hardware module to perform functions describedherein.

In some cases, aspects of the present disclosure may be described belowbased on the components of FIG. 2 .

FIG. 3 is a diagram illustrating resource elements including symbolsaccording to an embodiment.

According to an embodiment of FIG. 3 , the communication device mayperform wireless communication based on a resource block consisting ofresource elements in a wireless access network. In FIG. 3 , thehorizontal axis may represent a time domain (e.g., the x-axis mayrepresent time resources for wireless communications), and the verticalaxis may represent a frequency domain (e.g., the y-axis may representfrequency resources for wireless communications). A transmission unit(e.g., a minimum transmission unit) in the time domain may be referredto a symbol, and one symbol may be allocated to one time sequence. Aplurality of symbols may constitute a slot, and two slots may constituteone subframe. For example, in an LTE wireless access network, a lengthof a slot may be 0.5 ms, and a length of a subframe may be 1.0 ms.Further, a radio frame is a time domain unit consisting of tensubframes. The minimum transmission unit in the frequency domain is asubcarrier, and a bandwidth of the entire system transmission bandwidthmay include a plurality of subcarriers.

The basic unit of the resource in the time-frequency domain is aresource element (RE), which may be represented by a symbol index (e.g.,an orthogonal frequency division multiples (OFDM) symbol index) and asubcarrier index. A resource block (RB) (e.g., or a physical resourceblock (PRB)) may be defined by a plurality of symbols (e.g., a pluralityof consecutive OFDM symbols) in the time domain and by a plurality ofconsecutive subcarriers in the frequency domain.

FIG. 4 is a flowchart illustrating a method of calculating the firstphase difference PD1 and the second phase difference PD2, based on aplurality of previous signals, according to an embodiment, and FIG. 5 isa diagram of the phase difference calculating module 210 according to anembodiment.

With reference to FIGS. 4 and 5 , a communication device may calculatethe first phase difference PD1 and the second phase difference PD2,based on phases of a plurality of input signals. Specifically, a firstphase difference calculator 211 included in the phase differencecalculating module 210 may generate the first phase difference PD1, andthe second phase difference calculator 212 may generate the second phasedifference PD2.

In operation S10, the demodulator 21 may calculate as the first phasedifference PD1 as a difference between a phase of the first previoussignal and a phase of the second previous signal. At this time, thesecond previous signal may be a signal received prior to the firstprevious signal. According to an embodiment, the communication devicemay calculate the first phase difference PD1 between the phase of thefirst previous signal and the phase of the second previous signal in thefirst previous sequence receiving the first previous signal, and thefirst phase difference PD1 may be delayed by a certain sequence and maybe used to calculate the first likelihoods in the target sequence.

Specifically, according to an embodiment of FIG. 5 in which a targetsignal is received in a target sequence, the first phase differencecalculator 211 may calculate a difference between a phase TG of a targetsignal and a phase FB_PRV1 of a first feedback previous signal, whichhas been received prior to the target signal and provided as feedback(e.g., as feedback to the first phase difference calculator 211). Thatis, the first phase difference calculator 211 may generate a differencebetween a phase of a first previous signal and a phase FB_PRV2 of asecond feedback previous signal as the first phase difference PD1 in afirst previous sequence preceding a target sequence.

In operation S20, the demodulator 21 may calculate the second phasedifference PD2 between the target signal and the second previous signal.At this time, the second previous signal may be a signal received priorto the target signal by two or more sequences.

With reference to FIG. 5 , in the target sequence, the second phasedifference calculator 212 may receive the phase TG of the target signaland the phase FB_PRV2 of the second feedback previous signal, which hasbeen delayed for a certain sequence (e.g., two or more sequences) andprovided as feedback by a delay circuit 214. The second phase differencecalculator 212, which has received the phase TG of the target signal andthe phase FB_PRV2 of the second feedback previous signal, may output asthe second phase difference PD2 a difference between the phase TG of thetarget signal and the phase FB_PRV2 of the second feedback previoussignal. The delay circuit 214 may be a circuit configured to delay areceived signal for a certain sequence and provide the signal to thesecond phase difference calculator 212. For example, the delay circuit214, which has received the phase FB_PRV2 of the second feedbackprevious signal in the first previous sequence, may provide the phaseFB_PRV2 of the second feedback previous signal to the second phasedifference calculator 212 in a subsequent target sequence, and the delaycircuit 214, which has received the phase FB_PRV1 of the first feedbackprevious signal in the target sequence, may provide the phase FB_PRV1 ofthe first feedback previous signal to the second phase differencecalculator 212 in a sequence following the target sequence.

According to an embodiment, an accumulator 213 may at least temporarilystore received feedback phase differences generated up to the previoussequence and accumulate the phase differences generated up to theprevious sequence to generate a phase of a feedback previous signal. Forexample, the accumulator 213 may accumulate feedback phase differencesgenerated up to the first previous sequence after initiating thedemodulation operation, and generate the accumulated phase differencesas the phase FB_PRV1 of the first feedback previous signal in the targetsequence. At this time, the feedback phase differences received by theaccumulator 213 may be hard-decision phase differences HDP. Thehard-decision phase difference HDP is described in detail herein (e.g.,at least with reference to FIGS. 6 and 7 ).

According to an embodiment, the first phase difference calculator 211may calculate the first phase difference PD1 by subtracting the phaseFB_PRV1 of the first feedback previous signal and a reference phase REFfrom the phase TG of the target signal, and the second phase differencecalculator 212 may calculate the second phase difference PD2 bysubtracting the phase FB_PRV2 of the second feedback previous signal andthe reference phase REF from the phase TG of the target signal. That is,the first phase difference PD1 and the second phase difference PD2calculated in an n^(th) sequence, which is the target sequence, may berepresented by the following Equation 1.

$\begin{array}{l}{\Delta_{1}\varnothing_{\text{n}} = \varnothing_{\text{n}} - \text{f}\left( {\Delta\varnothing_{\text{n-1}}} \right) - \varnothing_{ref}} \\{\Delta_{2}\varnothing_{n} = \varnothing_{n} - f\left( {\Delta\varnothing_{n - 2}} \right) - \varnothing_{ref}}\end{array}$

Here, Δ₁Ø_(n) represents the first phase difference PD1, Δ₂Ø_(n)represents the second phase difference PD2, Ø_(n) represents the phaseTG of the target signal, ƒ(ΔØ_(n-1)) represents a phase FB_PRV1 of thefirst feedback previous signal, ƒ(Δ_(n-2)) represents a phase FB_PRV2of the second feedback previous phase, and _(ref) represents thereference phase REF.

FIG. 6 is a flowchart illustrating a method of calculating thehard-decision phase difference HDP according to an embodiment, and FIG.7 is a graph showing the hard-decision phase difference HDP of a phasedifference calculated according to an embodiment.

With reference to FIGS. 5 and 6 , in the first previous sequence, theaccumulator 213 may generate a phase of the second previous signal bysumming feedback hard-decision phase differences HDP up to the secondprevious sequence, and in the target sequence, the accumulator 213 maygenerate a phase of the first previous signal by summing feedbackhard-decision phase differences HDP up to the first previous sequence.

In operation S11, the accumulator 213 may obtain the hard-decision phasedifferences HDP of the signals received up to the second previoussequence. The hard-decision phase difference HDP may refer to a phase ofa symbol which has been hard-decided (e.g., a symbol phase to which theexpected phase difference EPD, determined by the demodulator 21 based ona target likelihood, corresponds to).

With reference to FIG. 7 , the expected phase difference EPD determinedby the demodulator 21 may not exactly correspond to a phase of eachsymbol. For example, a plurality of symbols may include four symbolseach allocated in a quadrant, and the demodulator 21 may determine asthe expected phase difference EPD a phase apart from a second symbol S2by θ. At this time, the demodulator 21 performing the hard-decisionoperation may determine as the second symbol S2 a symbol correspondingto the expected phase difference EPD and provide to the accumulator 213,as feedback, a phase corresponding to the second symbol S2 as thehard-decision phase difference HDP.

In operation S12, the accumulator 213 may sum hard-decision phasedifferences HDP of signals received in each sequence up to the secondprevious sequence after initiating the demodulation operation togenerate the phase FB_PRV2 of the second feedback previous signal.

The accumulator 213 may sum the hard-decision phase differences HDPgenerated in each sequence. For example, the accumulator 213 may add afeedback hard-decision phase difference HDP to a phase of a feedbackprevious signal generated in an immediately preceding sequence to updatethe phase of the feedback previous signal. The phase of the previoussignal to be updated may be represented by the following Equation 2.

$\begin{array}{l}{f\left( {\Delta\phi_{n - 1}} \right) = hard - decision\left( {\phi^{\prime}}_{n - 1} \right) + f\left( {\Delta\phi_{n - 2}} \right)} \\{f\left( {\Delta\phi_{n - 2}} \right) = hard - decision\left( {\phi^{\prime}}_{n - 2} \right) + f\left( {\Delta\phi_{n - 3}} \right)}\end{array}$

ƒ(ΔØ_(n-1)) represents a phase FB_PRV1 of the first feedback previoussignal, ƒ(ΔØ_(n-2)) represents a phase FB_PRV2 of the second feedbackprevious signal, ƒ(ΔØ_(n-3)) represents the third feedback previoussignal FB_PRV3, hard - decision(ϕ'_(n-1)) represents the hard-decisionphase difference HDP for the first previous signal, and hard -decision(ϕ'_(n-2)) represents the hard-decision phase difference HDP forthe second previous signal.

With reference to FIGS. 5 to 7 , the second phase difference calculator212 may receive the phase TG of the target signal and the phase FB_PRV2of the second feedback previous signal, and the accumulator 213 mayprovide to the second phase difference calculator 212 the phase PRV2_HDof the second feedback previous signal generated by adding up thehard-decision phase differences HDP or the phase PRV2_EPD of the secondfeedback previous signal generated by adding up the expected phasedifferences EPD.

According to an embodiment, the second phase difference PD2 generatedbased on the phase PRV2_HD of the second feedback previous signalgenerated by adding up the hard-decision phase differences HDP maygenerate more accurate phase difference by preventing error propagation,and accordingly, a symbol corresponding to a phase difference may beaccurately determined.

Generally, the phase of the feedback previous signal is not limited tothe phase generated by adding up the phase differences corresponding toprevious sequences by the accumulator 213, and it may be a phase of aninput signal sampled in a previous sequence.

FIG. 8 is a diagram illustrating signals that the phase differencecalculating module 210 may receive in each sequence according to anembodiment.

With reference to FIG. 8 , the accumulator 213, the first phasedifference calculator 211, and the second phase difference calculator212 may transmit and receive phases of a signal in a consecutive secondprevious sequence PRV2_SEQ, a first previous sequence PRV1_SEQ, and atarget sequence TG_SEQ. The first phase difference calculator 211 andthe second phase difference calculator 212 may receive phases of asignal through two input terminals, and may also receive through acommon input terminal a phase of a signal received from a transceiver ineach sequence.

According to an embodiment, the accumulator 213 may output a phase of afeedback previous signal generated according to embodiments of FIGS. 6and 7 . For example, in the second previous sequence PRV2_SEQ, theaccumulator 213 may output the phase FB_PRV3 of a third feedbackprevious signal (e.g., a third sequence preceding the second sequence)obtained by adding up the hard-decision phase differences HDP up to thethird previous sequence, output the phase FB_PRV2 of the second feedbackprevious signal obtained by adding up the hard-decision phasedifferences HDP up to the second previous sequence PRV2_SEQ in the firstprevious sequence PRV1_SEQ, and output the phase FB_PRV1 of the firstfeedback previous signal obtained by adding up the hard-decision phasedifferences HDP up to the first previous sequence PRV1_SEQ in the targetsequence TG_SEQ.

The first phase difference calculator 211 may receive a phase outputfrom the accumulator 213 through a first input terminal IN1, and receivea phase corresponding to each sequence received from the transceiverthrough a second input terminal IN2. For example, in the first previoussequence PRV1_SEQ, the first phase difference calculator 211 may receivethe phase FB_PRV2 of the second feedback previous signal through thefirst input terminal IN1, and receive the phase PRV1 of the firstprevious signal through the second input terminal IN2. In the targetsequence TG_SEQ, the first phase difference calculator 211 may receivethe phase FB_PRV1 of the first feedback previous signal through thefirst input terminal IN1, and receive the phase TG of the target signalthrough the second input terminal IN2.

The second phase difference calculator 212 may receive an output phaseof the accumulator 213 of the immediately preceding sequence from thedelay circuit through the first input terminal IN1, and receive a phaseof a signal corresponding to each sequence received from the transceiverthrough the second input terminal IN2. For example, in the firstprevious sequence PRV1_SEQ, the second phase difference calculator 212may receive the phase of the third feedback previous signal through thefirst input terminal IN1, and receive the phase PRV1 of the firstprevious signal through the second input terminal IN2. In the targetsequence TG_SEQ, the second phase difference calculator 212 may receivethe phase FB_PRV2 of the second feedback previous signal through thefirst input terminal IN1, and receive the phase TG of the target signalthrough the second input terminal IN2.

According to FIGS. 10 and 11 described below, when generating firstlikelihoods, the demodulator 21 may use the first phase difference PD1of an immediately preceding sequence through the delay circuit. Forexample, the demodulator 21 may use the first phase difference PD1generated in the first previous sequence PRV1_SEQ to calculate the firstlikelihoods in the target sequence TG_SEQ. At this time, the first phasedifference PD1 generated in the first previous sequence PRV1_SEQ may bea phase difference generated based on the phase FB_PRV2 of the secondfeedback previous signal and the phase PRV1 of the first previoussignal. Accordingly, in the target sequence TG_SEQ, the demodulator 21may calculate the first likelihood based on a first phase difference 81generated by the phase FB_PRV2 of the second feedback previous signaland the phase PRV1 of the first previous signal, and calculate thesecond likelihood, based on a second phase difference 82 generated bythe phase FB_PRV2 of the second feedback previous signal and the phaseTG of the target signal.

FIG. 9 is a flowchart illustrating a method of determining the expectedphase difference EPD or the expected symbol ES by calculating a targetlikelihood according to an embodiment, and FIGS. 10 and 11 are blockdiagrams illustrating a configuration of the phase-to-symbol likelihoodgenerating module 220 according to embodiments.

With reference to FIGS. 9 to 11 , the demodulator 21 may calculate firstlikelihoods LL1 and second likelihoods LL2, based on the first phasedifference PD1 and the second phase difference PD2, and determine theexpected phase difference EPD or the expected symbol ES by calculatingthe target likelihood, based on the first likelihoods LL1 and the secondlikelihoods LL2. An embodiment of FIG. 10 illustrates thephase-to-symbol likelihood generating module 220 configured to determinethe expected phase difference EPD, and an embodiment of FIG. 11illustrates the phase-to-symbol likelihood generating module 220configured to determine the expected symbol ES.

With reference to FIGS. 9 to 11 , in operation S30, first likelihoodgenerators 221 a and 221 b may calculate the first likelihoods LL1 thatthe first phase difference PD1 corresponds to each of a plurality ofsymbols. For example, when the plurality of symbols include foursymbols, the first likelihood generators 221 a and 221 b may generatefour first likelihoods LL1. That is, the first likelihood generators 221a and 221 b may calculate as the first likelihoods LL1 likelihoods thatthe first phase difference PD1 corresponds to first to fourth symbols S1to S4. According to an embodiment, the first likelihoods LL1 may becalculated based on a Euclidean squared distance between the first phasedifference PD1 and a phase corresponding to each symbol, and accordingto another embodiment, the first likelihoods LL1 that the first phasedifference PD1 corresponds to each symbol may be selected from a lookuptable based on the reliability of the first phase difference PD1.

According to an embodiment, delay circuits 223 a and 223 b may delay thefirst phase difference PD1 for a certain sequence from a sequence inwhich the first phase difference PD1 has been received and provide afirst delay phase difference DL_PD1 to the first likelihood generators221 a and 221 b. For example, the delay circuits 223 a and 223 b, whichhave received the first phase difference PD1 in the first previoussequence, may delay the first phase difference PD1 for a sequence andprovide the first delay phase difference DL_PD1 to the first likelihoodgenerators 221 a and 221 b. That is, with reference to FIG. 8 , thedelay circuits 223 a and 223 b may provide the first phase differencePD1, which is generated by the phase FB_PRV2 of the second feedbackprevious signal and the phase PRV1 of the first previous signal in thefirst previous sequence, to the first likelihood generators 221 a and221 b in the target sequence. Accordingly, in the target sequence, thefirst likelihood generators 221 a and 221 b may generate the firstlikelihoods LL1 based on the first phase difference PD1 between thefirst previous signal and the second previous signal.

In operation S40, the second likelihood generators 222 a and 222 b maycalculate the second likelihoods LL2 that the second phase differencePD2 corresponds to each of the plurality of symbols. For example, thesecond likelihood generators 222 a and 222 b may calculate as the secondlikelihoods LL2 likelihoods that the second phase difference PD2corresponds to the first to fourth symbols S1 to S4. According to anembodiment, the second likelihoods LL2 may be calculated based on aEuclidean squared distance between the second phase difference PD2 and aphase corresponding to each symbol, and according to another embodiment,the second likelihoods LL2 that the second phase difference PD2corresponds to each symbol may be selected from a lookup table based onthe reliability of the second phase difference PD2.

In operation S50, the second likelihood generators 222 a and 222 b mayreceive the first likelihoods LL1, and calculate target likelihoodsTGLL, based on the first likelihoods LL1 and the second likelihoods LL2.According to an embodiment, the first likelihoods LL1 may be likelihoodsthat a difference between the phase PRV1 of the first previous signaland the phase PRV2 of the second previous signal corresponds to eachsymbol and the second likelihoods LL2 may be likelihoods that adifference between the phase TG of the target signal and the phase PRV2of the second previous signal corresponds to each symbol. At this time,the target likelihoods TGLL may be likelihoods that the phase TG of thetarget signal and the phase PRV1 of the first previous signal correspondto each symbol.

Specifically, the second likelihood generators 222 a and 222 b mayreceive the first likelihood LL1 that the first phase difference PD1corresponds to a j^(th) symbol (j is a natural number), which is one ofthe plurality of symbols. To calculate a likelihood that a differencebetween the phase TG of the target signal and the phase PRV1 of thefirst previous signal corresponds to an i^(th) symbol (i is a naturalnumber), the second likelihood generators 222 a and 222 b may multiplythe second likelihood LL2 that the second phase difference PD2corresponds to a sum of the i^(th) symbol and the j^(th) symbol by thefirst likelihood LL1 that the first phase difference PD1 corresponds tothe j^(th) symbol (j is a natural number). That is, the secondlikelihood generator may calculate the likelihood that the first phasedifference PD1 is the j^(th) symbol and the difference between the phaseTG of the target signal and the phase PRV1 of the first previous signalcorresponds to the i^(th) symbol.

The second likelihood generators 222 a and 222 b may sum products of thefirst likelihood LL1 when the first phase difference PD1 corresponds toall symbols and the second likelihoods LL2 corresponding thereto tocalculate the likelihood that the difference between the phase TG of thetarget signal and the phase PRV1 of the first previous signalcorresponds to the i^(th) symbol, which may be represented by thefollowing Equation 3.

$Pr\left\{ {\Delta\phi_{n} = c_{i}} \right\} = {\sum\limits_{j = 0}^{2^{datarate} - 1}{Pr\left\{ {\Delta\phi_{n} = c_{i}\left| {\Delta\phi_{n - 1} = c_{j}} \right)} \right\} \cdot Pr\left\{ {\Delta\phi_{n - 1} = c_{j}} \right\}}}$

Here, Pr{Δϕ_(n) = c_(i)} represents the likelihood that the differencebetween the phase TG of the target signal and the phase PRV1 of thefirst previous signal corresponds to the i^(th) symbol, and Pr{Δϕ_(n) =c_(i)| Δϕ_(n-1) = c_(j)} represents the conditional likelihood that thedifference between the phase TG of the target signal and the phase PRV1of the first previous signal corresponds to the i^(th) symbol when thefirst phase difference PD1 corresponds to the j^(th) symbol. That is,Pr{Δϕ_(n) = c_(i)| Δϕ_(n-1) = c_(j)} may be the likelihood that thesecond phase difference PD2 corresponds to a symbol obtained bycombining the i^(th) symbol to the j^(th) symbol. Pr{Δϕ_(n-1) = c_(j)}may be the likelihood that the first phase difference PD1 is the j^(th)symbol.

For example, when the plurality of symbols include four symbols asillustrated in an embodiment of FIG. 7 , the second likelihoodgenerators 222 a and 222 b may sum products of four first likelihoodsLL1 and second likelihoods LL2 to calculate a likelihood that thedifference between the phase TG of the target signal and the phase PRV1of the first previous signal corresponds to the first symbol S1. Thesecond likelihood generators 222 a and 222 b may multiply the firstlikelihood LL1 that the first phase difference PD1 corresponds to thefirst symbol S1 and the second likelihood LL2 that the second phasedifference PD2 corresponds to the second symbol S2 and multiply thefirst likelihood LL1 that the first phase difference PD1 corresponds tothe second symbol S2 and the second likelihood LL2 that the second phasedifference PD2 corresponds to the third symbol S3. The second likelihoodgenerators 222 a and 222 b may multiply the first likelihood LL1 thatthe first phase difference PD1 corresponds to the third symbol S3 andthe second likelihood LL2 that the second phase difference PD2corresponds to the fourth symbol S4 and multiply the first likelihoodLL1 that the first phase difference PD1 corresponds to the fourth symbolS4 and the second likelihood LL2 that the second phase difference PD2corresponds to the first symbol S1. The second likelihood generators 222a and 222 b may sum all products of four first likelihoods LL1 and foursecond likelihoods LL2 to calculate the likelihood that the differencebetween the phase TG of the target signal and the phase PRV1 of thefirst previous signal corresponds to the first symbol S1.

The second likelihood calculators 222 a and 222 b may calculate thetarget likelihood TGLL that the difference between the phase TG of thetarget signal and the phase PRV1 of the first previous signalcorresponds to the i^(th) symbol and in a similar way, calculate thetarget likelihoods TGLL that the difference between the phase TG of thetarget signal and the phase PRV1 of the first previous signalcorresponds to all symbols.

In operation S60, the demodulator 21 may determine the expected phasedifference EPD or the expected symbol ES, based on the targetlikelihoods TGLL. The expected phase difference EPD may be an expectedvalue for the difference between the phase of the target signal and thephase PRV1 of the first previous signal generated based on the targetlikelihoods TGLL, and the expected symbol ES may be a symbolcorresponding to the expected phase difference EPD.

With reference to FIG. 10 , an axis value generator 225 a may receivethe target likelihoods TGLL and multiply a target likelihoodcorresponding to each of a plurality of symbols by a first axis valueand a second axis value of each symbol. The first axis value may be anX-axis value of each symbol, and the second axis value may be a Y-axisvalue of each symbol. For example, with reference to FIG. 8 , the axisvalue generator 225 a may multiply the target likelihood that the targetphase difference, which is a difference between the phase of the targetsignal and the phase PRV1 of the first previous signal, corresponds tothe first symbol S1 by 1, which is the X-axis value of the first symbolS1, and multiply the target likelihood that the target phase differencecorresponds to the first symbol S1 by 1, which is the Y-axis value ofthe first symbol S1. In this manner, the axis value generator 225 a maymultiply the target likelihoods TGLL that the target phase differencecorresponds to the second symbol S2 to the fourth symbol S4 by the firstaxis value and the second axis value.

The axis value generator 225 a may determine a first axis expected valueAV1 and a second axis expected value AV2 by summing products of thetarget likelihoods TGLL and each axis value corresponding to the targetlikelihoods TGLL per each axis. That is, the first axis expected valueAV1 and the second axis expected value AV2 may be represented by thefollowing Equation 4.

$\begin{array}{l}{I_{n} = cos\left( {\Delta\phi_{n}} \right) = {\sum\limits_{i = 0}^{2^{datarate} - 1}{cos\left( c_{i} \right) \cdot Pr\left\{ {\Delta\phi_{n} = c_{i}} \right\}}}} \\{Q_{n} = sin\left( {\Delta\phi_{n}} \right) = {\sum\limits_{i = 0}^{2^{datarate} - 1}{sin\left( c_{i} \right) \cdot Pr\left\{ {\Delta\phi_{n} = c_{i}} \right\}}}}\end{array}$

Here, I_(n) represents the first axis expected value AV1, Q_(n)represents the second axis expected value AV2, cos(c_(i)) represents thefirst axis value of the i^(th) symbol, and sin(c_(i)) represents thesecond axis value of the i^(th) symbol.

The axis value generator 225 a may provide the first axis expected valueAV1 and the second axis expected value AV2 to an arc-tangent calculator,and the arc-tangent calculator 227 a may output the expected phasedifference EPD by performing an arc-tangent operation on a ratio betweenthe first axis expected value AV1 and the second axis expected value AV2according to the following Equation 5.

$\Delta\phi_{n} = tan^{- 1}\left( \frac{Q_{n}}{I_{n}} \right)$

The symbol-phase providers 224 a and 226 a may provide phasescorresponding to each symbol to the first likelihood generator, thesecond likelihood generator, and the axis value generator 225 a.According to an embodiment, the first likelihood generator and thesecond likelihood generator may calculate a distance between the phasecorresponding to each symbol provided from the symbol-phase providers224 a and 226 a and the first phase difference PD1 as well as the secondphase difference PD2 when calculating a first distance and a seconddistance according to an embodiment of FIG. 13 described below.

According to an embodiment, the demodulator 21 may further include amultiplexer 228 a, and the multiplexer 228 a may output one of the firstphase difference PD1 and the expected phase difference EPD generated inthe target sequence based on a demodulating mode. For example, themultiplexer 228 a may output as a final phase difference the first phasedifference PD1 when the multiplexer 228 a receives a first demodulatingmode, and output as a final phase difference the expected phasedifference EPD when the multiplexer 228 a receives a second demodulatingmode. The first demodulating mode may be a mode in which a demodulationoperation is performed at a rapid rate by omitting the operation ofgenerating the expected phase difference EPD, and the seconddemodulating mode may be a mode in which the demodulation operation isperformed accurately by generating the expected phase difference EPD,based on the phase of a plurality of previous signals.

With reference to FIG. 11 , the demodulator 21 may include an expectedsymbol determiner 227 b, and the expected symbol determiner 227 b mayoutput the expected symbol ES for the target signal, based on an outputof a multiplexer 226 b. The multiplexer 226 b may output one of thetarget likelihood and the first likelihood according to the demodulatingmode.

For example, when the demodulator 21 receives the first demodulatingmode, the first likelihood generator 221 b may not receive the firstphase difference PD1 through the delay circuit, and generate the firstlikelihoods LL1 by receiving the first phase difference PD1 between thephase TG of the target signal and the phase PRV1 of the first previoussignal generated in the target sequence. In the first demodulating mode,the multiplexer 226 b may output the first likelihoods LL1 generated bythe first likelihood generator 221 b. When the demodulator 21 receivesthe second demodulating mode, the multiplexer 226 b may provide thetarget likelihoods TGLL to the expected symbol determiner 227 b. Themethod of determining the expected symbol ES based on the likelihoodsreceived by the expected symbol determiner 227 b will be described laterwith reference to FIG. 12 .

The symbol-phase providers 224 a and 225 a may provide phasescorresponding to each symbol to the first likelihood generator 221 b andthe second likelihood generator 222 b. According to an embodiment, thefirst likelihood generator 221 b and the second likelihood generator 222b may calculate a distance between the phase corresponding to eachsymbol provided from the symbol-phase providers 224 b and 225 b and thefirst phase difference PD1 as well as the second phase difference PD2when calculating a first distance and a second distance according to anembodiment of FIG. 13 described below.

FIG. 12 is a block diagram illustrating configuration of the expectedsymbol determiner 227 b according to an embodiment.

With reference to FIG. 12 , the expected symbol determiner 227 b mayinclude a permutation circuit 227_1, a divider 227_2, and a logcalculator 227_3, and determine a symbol corresponding to the targetlikelihoods TGLL by bit. The permutation circuit 227_1 may determine theexpected symbol ES, based on a combination of target likelihoods TGLLpredetermined per bit.

For example, when a plurality of symbols include four symbols accordingto an embodiment of FIG. 7 , data of the first symbol S1 may be ‘00’,data of the second symbol S2 may be ‘01’, data of the third symbol S3may be ‘11’, data of the fourth symbol S4 may be ‘10’, and thepermutation circuit 227_1 may receive first to fourth target likelihoodsTGLL1 to TGLL4 corresponding to each symbol. When the expected symboldeterminer 227 b outputs a bit of the expected symbol ES from the mostsignificant bit (MSB), the expected symbol determiner 227 b may add thefirst target likelihood TGLL1 to the second target likelihood TGLL2corresponding to each symbol by putting the first symbol S1 and thesecond symbol S2 of which MSB is 1, together as one combination. Theexpected symbol determiner 227 b may put the third symbol S3 and thefourth symbol S4 of which the MSB is 0 together as a combination and addthe third target likelihood TGLL3 to the fourth target likelihood TGLL4corresponding toe each symbol.

In this manner, the permutation circuit 227_1 may provide to the divider227_2 a likelihood of a bit being 0 and a likelihood of a bit being 1,based on combinations of the target likelihoods TGLL defined by bit fromthe MSB to the least significant bit (LSB). The divider 227_2 mayreceive a target likelihood of the bit being 0 and a target likelihoodof the bit being 1 from the permutation circuit 227_1 and provide thetwo likelihoods to the log calculator 227_3. The log calculator 227_3may generate bits of the expected symbol ES based on the likelihood ofbit being 0 and the likelihood of bit being 1 received from the divider.

FIG. 13 is a flowchart illustrating a method of calculating firstlikelihoods and second likelihoods according to an embodiment.

With reference to FIG. 13 , each of the first likelihood generator andthe second likelihood generator may receive the first phase differencePD1 and the second phase difference PD2, and calculate the firstlikelihoods and the second likelihoods based on a distance between eachphase difference and each of the plurality of symbols.

In operation S311, the first likelihood generator may calculate adifference between the first phase difference PD1 and the phasecorresponding to each of the plurality of symbols as the firstdistances. The first distance may be a Euclidean squared distancebetween the first phase difference PD1 and a phase corresponding to asymbol, which may be represented by the following Equation 6.

d_(1, j)² = 2(1 − cos(|Δ₁⌀_(n − 1) − c_(j)|))

Here, d_(1,j) represents the first distance between the first phasedifference and the phase corresponding to the j^(th) symbol, Δ₁Ø_(n-1)represents the received first phase difference PD1 delayed by the delaycircuit, and, c_(j) represents the phase corresponding to the j^(th)symbol. The first likelihood generator may calculate the Euclideansquared distance between the phases corresponding to all symbols and thefirst phase difference PD1.

In operation S312, the first likelihood generator may calculate thefirst likelihoods, based on the first distances. For example, the firstlikelihood generator may calculate the first likelihoods according tothe following Equation 7.

$Pr\left\{ {\Delta\phi_{n - 1} = c_{j}} \right\} = \frac{1}{\sqrt{2\pi\sigma^{2}}}exp\left( {- \frac{d_{1,j}^{2}}{2\sigma^{2}}} \right)$

Here, Pr{Δϕ_(n-1) = c_(j)} represents the first likelihood, and

d_(1, j)²

represents the first distance which is a Euclidean squared distanceregarding the jth symbol and the first phase difference PD1.

In operation S313, the second likelihood generator may calculate adifference between the second phase difference PD2 and the phasecorresponding to each of the plurality of symbols as the seconddistances. The second distance may be a Euclidean squared distancebetween the second phase difference PD2 and a phase corresponding to asymbol, which may be represented by the following Equation 8.

d_(2, i, j)² = 2(1 − cos(|Δ₂⌀_(n) − (c_(i) + c_(j))|))

Here, d₂,_(i),_(j) represents the second distance between the secondphase difference and the phase corresponding to a symbol into which thei^(th) symbol and the j^(th) symbol is combined, Δ₂Ø_(n) represents thesecond phase difference PD2, and c_(i) + c_(j) represents the phasecorresponding to the symbol into which the i^(th) symbol and the j^(th)symbol is combined. The second likelihood generator may calculate theEuclidean squared distance between the phases corresponding to allsymbols and the second phase difference PD2.

In operation S314, the second likelihood generator may calculate thesecond likelihoods, based on the second distances. For example, thesecond likelihood generator may calculate the second likelihoodsaccording to the following Equation 9.

$Pr\left\{ {\Delta\phi_{n} = c_{i}\left| {\Delta\phi_{n - 1} = c_{j}} \right)} \right\} = \frac{1}{\sqrt{2\pi\sigma^{2}}}exp\left( {- \frac{d_{2,i,j}^{2}}{2\sigma^{2}}} \right)$

Here, Pr{Δϕ_(n) = c_(i)| Δϕ_(n-1) = c_(j)} represents the secondlikelihood, and

d_(2, i, j)²

represents the second distance, which is a Euclidean squared distanceregarding the symbol obtained by adding the i^(th) symbol to the j^(th)symbol and the second phase difference PD2.

FIG. 14 is a flowchart illustrating a method of selecting at least someof first likelihoods and second likelihoods from a lookup tableaccording to an embodiment.

With reference to FIG. 14 , at least some of the first likelihoods andthe second likelihoods may be selected from the lookup tables accordingto FIG. 13 and other embodiments. The lookup table may be a table oflikelihood values corresponding to reliability of the first phasedifference PD1 and the second phase difference PD2 prestored in a memoryof the communication device, and the demodulator 21 may load likelihoodvalues stored in the lookup table from the memory.

In operation S312, the first likelihood generator may calculate thereliability of the first phase difference PD1. The first phasedifference PD1 may be formed of data consisting of a series of bits, andthe first likelihood generator may determine the reliability of thefirst phase difference PD1 according to the configuration of the bits.For example, when the first phase difference PD1 includes nine bits, thefirst likelihood generator may calculate the reliability of the firstphase difference PD1 according to the following Equation 10.

$\gamma_{\Delta\phi} = \left\{ \begin{matrix}{\Delta\phi\left\lbrack {5:0} \right\rbrack,if\Delta\phi\lbrack 6\rbrack = 0} \\{127 - \Delta\phi\left\lbrack {5:0} \right\rbrack,otherwise}\end{matrix} \right)$

Here, γ_(Δϕ) represents the reliability of the phase difference, andΔϕ[5:0] represents six bits of the phase difference from the LSB. Thatis, the reliability of the phase difference may have a greater value asthe phase difference approaches a phase corresponding to each symbol,and have a smaller value as the phase difference approaches a decisionboundary. According to an embodiment of FIG. 7 , the decision boundarymay be an X-axis and a Y-axis. According to Equation 10, when sevenbits(Δϕ[6:0]) from the LSB of the phase difference include ‘1000000’ and‘0111111,’ the phase difference most nearly approaches the phasecorresponding to the symbol, and the reliability of the phase differencemay be 63, which is the greatest value.

The reliability according to one or more embodiments of the presentdisclosure is not limited to Equation 10, and the reliability of thephase difference in the EDR3 mode may be calculated according to thefollowing Equation 11.

$\gamma_{\Delta\phi} = \left\{ \begin{matrix}{\Delta\phi\left\lbrack {4:0} \right\rbrack,if\Delta\phi\lbrack 5\rbrack = 0} \\{63 - \Delta\phi\left\lbrack {4:0} \right\rbrack,otherwise}\end{matrix} \right)$

In operation S322, the first likelihood generator may select a firstlikelihood corresponding to the reliability of the first phasedifference PD1 from the lookup table based on the reliability of thefirst phase difference PD1. For example, the lookup table in the EDR2mode and EDR3 mode may be defined as the following Equation 12.

$\begin{matrix}{LUT_{EDR2} = \left\lbrack {161820\text{22 23 25 26 27 28 29 30 31}} \right\rbrack} \\{LUT_{EDR3} = \left\lbrack {1620\text{23 26 28 29 30 31}} \right\rbrack}\end{matrix}$

Here, LUT_(EDR2) represents a lookup table in the EDR2 mode, andLUT_(EDR3) represents a lookup table in the EDR3 mode.

The first likelihood generator may generate according to the followingEquation 13 a first likelihood corresponding to the reliability of thefirst phase difference PD1 when the first phase difference PD1 is withinthe decision boundary corresponding to the i^(th) symbol.

$\Pr\left\{ {\Delta\varphi = c_{\text{i}}} \right\} = \left\{ \begin{matrix}{LUT_{EDR2}{\left\lbrack \gamma_{\Delta\varphi} \right\rbrack/{32,\,\text{if 0} \leq \gamma_{\Delta\varphi} \leq 8}}} \\{LUT_{EDR2}{\lbrack 9\rbrack/{32,\,\text{if 9} \leq \gamma_{\Delta\varphi} \leq 10}}} \\{LUT_{EDR2}{\lbrack 10\rbrack/{32,\,\text{if 11} \leq \gamma_{\Delta\varphi} \leq 12}}} \\{LUT_{EDR2}{\lbrack 11\rbrack/{32,\,\text{if 13} \leq \gamma_{\Delta\varphi} \leq 17}}} \\{1,\text{otherwise}}\end{matrix} \right)$

At this time, the likelihood that the first phase difference PD1corresponds to the j^(th) symbol adjacent to the i^(th) symbol may berepresented by the following Equation 14.

Pr{Δϕ = c_(j)} = 1 − Pr{Δϕ = c_(i)}

In some examples, the first likelihood according to one or moreembodiments of the present disclosure is not limited to Equations 13 and14, and some of the first likelihoods in the EDR3 mode may be calculatedaccording to the following Equation 15.

$\begin{array}{l}{\text{Pr}\left\{ {\Delta\phi = \text{c}_{\text{i}}} \right\} = \left\{ \begin{array}{l}{\text{LUT}_{\text{EDR3}}\left\lbrack \gamma_{\Delta\phi} \right\rbrack\text{/}32,\text{if 0} \leq \gamma_{\Delta\phi} \leq 6} \\{\text{LUT}_{\text{EDR3}}\lbrack 7\rbrack\text{/}32,\text{if 7} \leq \gamma_{\Delta\phi} \leq 8} \\{1,\text{otherwise}}\end{array} \right)} \\{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{Pr}\left\{ {\Delta\phi = \text{c}_{\text{j}}} \right\} = 1 - \text{Pr}\left\{ {\Delta\phi - \text{c}_{\text{i}}} \right\}}\end{array}$

In operation S412, the second likelihood generator may calculate thereliability of the second phase difference PD2, based on the secondphase difference PD2, and in operation S422, the second likelihoodgenerator may select the second likelihood corresponding to thereliability of the second phase difference PD2 from the lookup table.The second likelihood generator may calculate the reliability of thesecond phase difference PD2 and the second likelihood in the same way asthe first likelihood generator, and thus, detailed descriptions thereonare omitted.

The first likelihood generator and the second likelihood generator maygenerate the first likelihoods and the second likelihoods (e.g., asdescribed in more detail herein, for example, with reference to FIGS. 13and 14 , but the techniques described herein are not limited thereto),and any one of the first likelihood generator and the second likelihoodgenerator may generate the likelihoods (e.g., according to an embodimentof FIG. 13 while the other may generate the likelihoods according to anembodiment of FIG. 14 , for example).

FIG. 15 is a block diagram illustrating components of a communicationdevice according to an embodiment.

With reference to FIG. 15 , a wireless communication device 1000 mayinclude an application processor (AP) 1100, a memory 1200, a display1300, and a radio frequency (RF) module 1410. In addition to this, thewireless communication device 1000 may further include variouscomponents such as a lens, a sensor, an audio module, etc.

In some aspects AP 1100 may represent or include an intelligent hardwaredevice, (e.g., a general-purpose processing component, a digital signalprocessor (DSP), a central processing unit (CPU) 1110, a graphicsprocessing unit (GPU), a microcontroller, an application specificintegrated circuit (ASIC), a field programmable gate array (FPGA), aprogrammable logic device, a discrete gate or transistor logiccomponent, a discrete hardware component, or any combination thereof).In some cases, the AP 1100 may be configured to operate a memory arrayusing a memory controller. In other cases, a memory controller isintegrated into the processor. In some cases, the AP 1100 is configuredto execute computer-readable instructions stored in a memory to performvarious functions. In some embodiments, AP 1100 includes special purposecomponents for modem processing, baseband processing, digital signalprocessing, or transmission processing.

Examples of a memory device include random access memory (RAM),read-only memory (ROM), or a hard disk. Examples of memory devicesinclude solid state memory and a hard disk drive. In some examples,memory is used to store computer-readable, computer-executable softwareincluding instructions that, when executed, cause a processor to performvarious functions described herein. In some cases, the memory contains,among other things, a basic input/output system (BIOS) which controlsbasic hardware or software operation such as the interaction withperipheral components or devices. In some cases, a memory controlleroperates memory cells. For example, the memory controller can include arow decoder, column decoder, or both. In some cases, memory cells withina memory store information in the form of a logical state.

The AP 1100 may be implemented as a System-on-Chip (SoC) and include aCPU 1110, RAM 1120, a power management unit (PMU) 1130, a memoryinterface (I/F) 1140, a display controller (DCON) 1150, a communicationprocessor 1160, and a system bus 1170. The AP 1100 may further includevarious intellectual properties (IPs) in addition to the above. The AP1100 may be referred to as a ModAP as the functions of a communicationprocessor chip are integrated into the AP 1100.

The CPU 1110 may generally control the operations of the AP 1100 and thewireless communication device 1000. The CPU 1110 may control theoperations of each component of the AP 1100. The CPU 1110 may also beimplemented by a multi-core. The multi-core refers to a computingcomponent having two or more independent cores.

The RAM 1120 may temporarily store programs, data, or instructions. Forexample, the programs and/or data stored in the memory 1200 may betemporarily stored in the RAM 1120 according to the control or bootingcode of the CPU 1110. The RAM 1120 may be implemented as dynamic randomaccess memory (DRAM) or static random access memory (SRAM).

The PMU 1130 may control the power of each component of the AP 1100. ThePMU 1130 may also determine operation situations of each component ofthe AP 1100 and control the operations.

The memory I/F 1140 may control the overall operations of the memory1200 and also control the data exchange between each component of the AP1100 and the memory 1200. The memory I/F 1140 may write data on thememory 1200 or read data from the memory 1200 according to a request ofthe CPU 1110.

The display controller 1150 may transmit to the display 1300 image datato be displayed on the display 1300. The display 1300 may be implementedas a flat display or a flexible display such as a liquid crystal display(LCD), an organic light emitting diode (OLED) display, etc. A display1300 may comprise a conventional monitor, a monitor coupled with anintegrated display, an integrated display (e.g., an LCD display), orother means for viewing associated data or processing information. Insome aspects, output devices other than the display 1300 may be used,such as printers, other computers or data storage devices, and computernetworks.

The communication processor 1160 may be properly modulate data to betransmitted and recover received data for wireless communication. Thecommunication processor 1160 may perform digital communication with theRF module 1410.

The RF module 1410 may convert a high frequency signal received throughan antenna into a low frequency signal, and transmit the low frequencysignal to the communication processor 1160. In addition, the RF module1410 may convert a low frequency signal received from the communicationprocessor 1160 into a high frequency signal, and transmit the highfrequency signal to the outside of the wireless communication device1000 through an antenna. In addition, the RF module 1410 may amplify orfilter a signal.

The RF module 1410 according to an embodiment of the present disclosuremay determine a symbol of a signal received through DPSK, and at thistime, a symbol of a target signal received in a target sequence may bedetermined based on phases of previous signals received in a pluralityof previous sequences.

In some aspects, software may include code to implement one or moreaspects of the present disclosure. Software may be stored in anon-transitory computer-readable medium such as system memory or othermemory. In some cases, the software may not be directly executable bythe processor but may cause a computer (e.g., when compiled andexecuted) to perform functions described herein.

While one or more aspects of techniques described herein have beenparticularly shown and described with reference to embodiments thereof,it will be understood that various changes in form and details may bemade therein without departing from the spirit and scope of thefollowing claims.

1. A method of determining a symbol according to a phase differencebetween input signals input in order of time, the method comprising:calculating a first phase difference between a phase of a first previoussignal and a phase of a second previous signal, wherein the firstprevious signal is received prior to a target signal, and wherein thesecond previous signal is received prior to the first previous signal;calculating a second phase difference between a phase of the targetsignal and the phase of the second previous signal; calculating, basedon the first phase difference and the second phase difference, targetlikelihoods that a phase difference between the target signal and thefirst previous signal corresponds to each of a plurality of symbols; anddetermining, based on the calculated target likelihoods, an expectedsymbol for the target signal or an expected phase difference between thetarget signal and the first previous signal.
 2. The method of claim 1,further comprising: obtaining hard-decision phase differences for one ormore received signals up to the second previous signal; and determiningthe phase of the second previous signal by adding up the hard-decisionphase differences.
 3. The method of claim 1, wherein the calculating ofthe target likelihoods comprises: calculating a plurality of firstlikelihoods that the first phase difference corresponds to each of theplurality of symbols; and calculating a plurality of second likelihoodsthat the second phase difference corresponds to each of the plurality ofsymbols.
 4. The method of claim 3, wherein the calculating of the firstlikelihoods comprises calculating a reliability of the first phasedifference based on a code corresponding to the first phase difference,and the calculating of the second likelihoods comprises calculating areliability of the second phase difference, based on a codecorresponding to the second phase difference.
 5. The method of claim 4,wherein: the calculating of the first likelihoods comprises: selecting afirst likelihood corresponding to the reliability of the first phasedifference from a lookup table; and determining the selected firstlikelihood as at least some of the first likelihoods, and thecalculating of the second likelihoods comprises: selecting a secondlikelihood corresponding to the reliability of the second phasedifference from the lookup table; and determining the selected secondlikelihood as at least some of the second likelihoods.
 6. The method ofclaim 3, wherein: the calculating of the first likelihoods comprises:calculating first distances between the first phase difference and aphase corresponding to each of the plurality of symbols; and calculatingthe first likelihoods based on the first distances, and the calculatingof the second likelihoods comprises: calculating second distancesbetween the second phase difference and the phase corresponding to eachof the plurality of symbols; and calculating the second likelihoods,based on the second distances.
 7. The method of claim 6, wherein thefirst distances comprise a Euclidean squared distance between the phasecorresponding to each of the plurality of symbols and the first phasedifference, and the second distances comprise a Euclidean squareddistance between the phase corresponding to each of the plurality ofsymbols and the second phase difference.
 8. The method of claim 3,wherein the calculating of the target likelihoods comprises: multiplyinga likelihood that the first phase difference corresponds to a firstsymbol of the plurality of symbols by a likelihood that the second phasedifference corresponds to a symbol obtained by combining the firstsymbol to a second symbol; and determining the target likelihood thatthe phase difference between the target signal and the first previoussignal corresponds to the second symbol by summing products of the firstlikelihood and the second likelihood when the first symbol correspondsto each of the plurality of symbols.
 9. The method of claim 8, whereinthe determining of the expected phase difference or the expected symbolfor the target signal comprises determining the expected symbol based ona combination of the target likelihoods predetermined per bit.
 10. Themethod of claim 8, wherein the determining of the expected phasedifference or the expected symbol for the target signal comprises:determining a first axis expected value and a second axis expectedvalue, based on the target likelihood when the second symbol correspondsto each of the plurality of symbols; and determining the expected phasedifference, based on the first axis expected value and the second axisexpected value.
 11. The method of claim 10, wherein the determining ofthe first axis expected value and the second axis expected valuecomprises: determining the first axis expected value by summing productsof the target likelihood corresponding to each of the plurality ofsymbols and a first axis value; and determining the second axis expectedvalue by summing products of the target likelihood corresponding to eachof the plurality of symbols and a second axis value.
 12. A method ofdetermining a symbol corresponding to an input signal, the methodcomprising: generating a first phase difference between a first inputsignal and a previous signal, wherein the first input signal is input ina previous sequence prior to a target sequence, and wherein the previoussignal is received prior to the previous sequence; generating a secondphase difference between a second input signal and the previous signal,wherein the second input signal is input in the target sequence; anddetermining an expected phase difference between the second input signaland the first input signal based on the first phase difference and thesecond phase difference.
 13. The method of claim 12, further comprising:obtaining hard-decision phase differences for one or more signalsreceived prior to receiving the previous signal; and determining a phaseof the previous signal by summing the hard-decision phase differences.14. The method of claim 12, wherein the determining of the expectedphase difference comprises: calculating target likelihoods that a phasedifference between the second input signal and the first input signalcorresponds to each of a plurality of symbols based on the first phasedifference and the second phase difference; and determining the expectedphase difference based on the target likelihoods and a phase of a symbolcorresponding to each target likelihood.
 15. The method of claim 14,wherein the calculating of the target likelihoods comprises: calculatinga plurality of first likelihoods that the first phase differencecorresponds to each of the plurality of symbols; and calculating aplurality of second likelihoods that the second phase differencecorresponds to each of the plurality of symbols.
 16. The method of claim15, wherein the calculating of the first likelihoods comprisescalculating a reliability of the first phase difference, based on a codecorresponding to the first phase difference, and the calculating of thesecond likelihoods comprises calculating a reliability of the secondphase difference, based on a code corresponding to the second phasedifference.
 17. The method of claim 16, wherein: the calculating of thefirst likelihoods comprises: selecting a first likelihood correspondingto the reliability of the first phase difference from a lookup table;and determining the selected first likelihood as at least some of thefirst likelihoods, and the calculating of the second likelihoodscomprises: selecting a second likelihood corresponding to thereliability of the second phase difference from the lookup table; anddetermining the selected second likelihood as at least some of thesecond likelihoods.
 18. The method of claim 15, wherein: the calculatingof the first likelihoods comprises: calculating first distances betweenthe first phase difference and a phase corresponding to each of theplurality of symbols; and calculating the first likelihoods based on thefirst distances, and the calculating of the second likelihoodscomprises: calculating second distances between the second phasedifference and a phase corresponding to each of the plurality ofsymbols; and calculating the second likelihoods, based on the seconddistances. 19-21. (canceled)
 22. A communication device comprising: afirst phase difference calculator configured to calculate a first phasedifference between a phase of a first previous signal and a phase of asecond previous signal, wherein the first previous signal is receivedprior to a target signal, and wherein the second previous signal isreceived prior to the first previous signal; a second phase differencecalculator configured to calculate a second phase difference between aphase of the target signal and the phase of the second previous signal;a target likelihood generator configured to generate target likelihoodsthat a phase difference between the target signal and the previous firstprevious signal corresponds to each of a plurality of symbols based onthe first phase difference and the second phase difference; and anexpected value determiner configured to determine, based on the targetlikelihoods, an expected symbol for the target signal or an expectedphase difference between the target signal and the first previoussignal.
 23. (canceled)
 24. The communication device of claim 22, whereinthe target likelihood generator comprises: a first likelihood generatorconfigured to calculate a plurality of first likelihoods that the firstphase difference corresponds to each of the plurality of symbols; and asecond likelihood generator configured to calculate a plurality ofsecond likelihoods that the second phase difference corresponds to eachof the plurality of symbols. 25-30. (canceled)